ML20217N719
| ML20217N719 | |
| Person / Time | |
|---|---|
| Site: | Crane  |
| Issue date: | 03/28/1998 |
| From: | EQE ENGINEERING CONSULTANTS (FORMERLY EQE ENGINEERING |
| To: | |
| Shared Package | |
| ML20217N635 | List: |
| References | |
| 50097.05-01, 50097.05-1, 50097.05-R, 50097.05-R00, NUDOCS 9805050406 | |
| Download: ML20217N719 (28) | |
Text
/[38 CALCULATION COVER SHEET
^ w%sa:MEMa# mage %dt#W4Ma@nt%#%t#CRWWMuuhrunW?ne Tacw t:Se U+ %. ; cum asagsg Calculation No.:
Project:
T M I -'i IPEE E Calculation
Title:
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References:
l Attachments:
b bd b Total Number of Pages (Including Cover Sheet) 2
^P Nu e De Description of Revision Originator Checker Approver 7
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j JOB NO. NN #I JOB TMI-I MEEb BY dT DATE )$k9[_
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i3/2p A-z BWSTank Respons,.3 Calculations:
This MATHCAD ternplate computes the response parameters which are needed in performing a tank evaluation j
per EPRI NP-6041 methodology for vertical flat bottom tanks. Inputs required are an earthquake, and the necessary tank parameters. Base units are feet, seconds, and pounds.
I i
Derived Units:
d kips 1000 lbf hzs1see ksis1000 psi Define Tank Geometry:
R := 16.5 A NominalInner Tank Radius M := 52 A Height to Maximum Water Elevation tb := 0.25 in Bottom Plate Thickness td := 0.25 in Dorta Thickness h := 8.67 ft Estimated Clearance between Peak of Dome to Spring Line d
nrings := 3 Nurnber of different diameter rings composing the tank shell (0.421) t := 0.338, in Shell Thickness at Each Ring from Bottom of The Tank to The Top.
[0.25 )
Avwe~
0,37I" ( v.Jof
~
f 8.67 )
Hr :=
17.33 ft Height of Each Ring Measured from The Bottom of The Tank to The Top.
{ 26 )
l Define Anchorace Details:
n := 40 Number of Equally Spaced Anchor Bolts
( := 2.0 in Anchor Bolt Diameter l-WHT_ TANK.MCD 4
1:27 PM
ev/a/
h-3 i
Define Material Properties:
E, := 28.010'. psi Young's Modulus for Shell Material o := 0.30 Poisson's Ratio l
y i := 62.4.5 Unit Weight for Content Uquid -
1 3
l ft 7 s := 0.284.lbf Unit Weight for shell material 3
in l
r i := 3.2510. psi Bulk Modulus of Fluid,3.25x10"5 psi for water 8
Eb := 2810'. psi Young's Moduluis for Bolt Material EPA := 0.8.g (This the PGA of the soil outcrop response spectrum) l i
j Compute averaae shell thickness. and total shell helaht l
i := 1..nrings H :=
Hr H, = 52 ft s
3 l
t; Hr; t, :=
- t, = 0.3078 in l
H, Define Dimensionless Parameters from Refs. 2 and 4:
Obtain Cwi from Reference 2, Table 7.4:
H Parameters needed for table 7.4
= 3.1515
= 0.002 R
R Readeff value for Cwl:
C y := 0.096 l.
WHT_ TANK.MCD S
1:27 PM 1
l
/f/3$
1 A-4
\\
l Tank Weiaht and C.G. Components:
Note that the distance to the component C.G. is measured from the bottom of the tank.
(Shell)
(Bottom Plate) j := 1..nrings b := (n R ) tb'T s 2
W l
W, ':= 2 n R 7, Hr, t, Wb = 8.74 kip W, := { W, i
tb X
W, = 67.9 kip b*2 Hr l
j Hr,-(isj)-
Xb =0.0104 A C8 :=
i
{W, eg; l
X,=I S
l X, = 23.17 A (Dome)
(Liquid) i f
2 2
2 Wh :: nR R,3 td7s Ww:=nR Hyj 3
W = 9.88 kip
.W
= 2.775 10 kip h
w w := E Xh :=H +
X s
3 2
l' Xh = 54 89' A X, = 26 A Fluid Hydrostatic Pressure:
Pst 71 H Maximum fluid pressure occurs at base of tank Pst = 22.53 psi l
i
)
WHT_ TANK.MCD 6
1:27 PM l
_j
llhi A-T
' Compute Horizontallmouisive Mode Response:
Impulsive Mode Frequency:
8 C g := C w j-C y =0.0959 (Reference 1, equation H-2)
II
{
Cy E,g f g := 2 nII 5 (y3) f; = 4.77 hz Read the spectral acceleration at this frequency from the soil outcrop response spectra, damping for the impulsive mode maybe taken as about 5%.
S g := 1.13-g Compute Weight of fluid effective in the impulsive Mode, and its corresponding C.G.:
tanh 1.732-W; := if Es$,
"I,1.0 - 0.436 E W, (Ref. 3, Eqn. C3500-1,-2. 3,-4)
R2 1.732E H
X :=if E52,0.375,0.5- 0.188 b 11 (Ref. 3, Eqn. C3500-1,-2,-3,-4) j i
(R 2 Hj W = 2.391 10' kip X =22.898 fi Compute impulsive Mode Base Shear and Overturning Moment:
S ah(W+W,+W;)
(Ref.1, Eqn. H-3)
V :=
i h
S Ss g :=
-(W 'Xh + W, X, + W X ;).
(Ref.1, Eqn. H-4)
M h
j B
8 V = 2.79*10 kip y
4 M g = 6.426 10 kipfi Estimate hydrodynamic fluid pressure on the tank at the bottom plate S
W ;.X ; ah (Ref.1, egn. H-8: Note this is conservative at g
P;:=
fluid depths less than about 0.1S*H) 2 1.36-R 11 P = 7.081 psi WHT_ TANK.MCD 7
1:27 PM
1 i
t7 M A-b i
l ComDute Horizontal Convective fSloshinal Mode Response:
Convective Mode frequency 1
'f ft )
2
]
f (Ref.1, eqn. H-10) f :=
-tanh 1.835 E e
,(
R
}
(
R f = 0.3 hz e
Use site specific response spectrum to find the Spectral Acceleration at this frequency, damping for the convective mode response is primarily fluid controlled and is estimated to be about 0.5%.
Scc := 0.1 g (conservative estimate)
Compute Weight of Fluid acting in the convective mode and its C.G. location
'f i
f 0.46 RHjl tanh 1.835 H Wc :=
W (Ref.1. egn. H-13) w
(
R
.i f
cosh 1.835 HI 1-1.0 R3 X e := 1.0-H (Ref.1, eqn. H-14) 1.835.
sinh 1.835 1
,R3
(
R.
3
(
W =405.0754 kip c
X = 43.0611 c
Compute Convective Mode Base Shear and Overturning Moment:
S" Vc := -..W (Ref.1, egn. H-13) c 8
M c :=
WX (Ref.1, egn. H-14) c c 8
V =40.5 kip c
3 M = 1.744 10 ft kip e
Compute Hydrodynamic Convective Pressure at fluid depth "y" y := H (This maximizes the hydrodynamic convective H-y Pressure.)
f i
0.267.W S w ac i
R 4
Pc :=
(Ref.1, egn. H-16) f gRH g
1.835 E t
R 3 P =0.0037 psi c
Compute the fundamental mode fluid slosh height S
h, := 0.837 R "
h, = 1.381 fi (Ref.1, egn. H-17) 8 WHT,_ TANK.MCD 8
1:27 PM
(
l tP N i
i A-7 ComDute Vertical Fluid Mode Response:
Compute the vertical fluid mode fundamental frequency f := 1 - 71 ( 2 R 1I y
+-
f = 5.92 hz (Ref. 3, eqn. C3500-13) y 4 11 g
t E, cjj 3
i Compute the hydrodynamic vertical fluid response mode pressure, based on a tank on a rigid foundation, note this pressure is also at y=H, which maximizes p.
S,y := 1.13.g (read off the soil outcrop response spectra)
N-Py := 0.8 y j H cos P = 20.3701 psi y
g 2( 11 j,
Combine Individual Mode Responses to aet Total Seismic Demand:
l Base Shear:
Overturning Moment i
2 Vtot
- Yi+V Mtot:= M g+M c
c Vtot = 2.7910' kip Mtot = 6.429 10 kipfi 4
l Fluid Pressures:
2 2
Psh := Pi +p Total Horizontal Seismic Response c
Pcma := Pst + Psh + 0.4 P Maximum and minimum compression zone pressures at the time of y
maximum base moment. (Ref.1, eqn. H-22)
Pcmin := Pst + Psh - 0.4 P y Ptmin := Pst - Psh - 0.4 P Maximum and minimum tension zone fluid pressure at the time of y
Ptmax.= Pst - Psh + 0.4 P maximum base moment (Ref.1, egn. H-23) y P
=Pst - 0.4 P Minimum average fluid pressure on the base plate av8 y
l at the time of maximum base shear (Ref.1. eqn H-14)
P
= 37.76 psi Ptmin = 7.3 psi.
cmax Pcmin = 21.47 psi Ptmax = 23.6 psi l
Pavg " I4'39 'P8i Expected minimum total effect weight of the tank shell acting on the base at $ 2 time of the maximum moment and base shear:
f I
te : (W + W ).' 1 - 0.4 2 EPA l
W h
s 1
(Ref.1, eqn. H-26) i 3 gj Wte = 61.2 kip Wh = 9.88 kip W = 67.9 kip s
WHT_, TANK.MCD 9
1:27 PM l
~
ESE ECE INTERNATIONAL If A SHEET NO. O f
- " " ' ^ ~ ' ' '
JOB NO. ['* 97 #[ JOB IMI~ l rbbGb BY WNT DATE b3 8 3
CALC. NO.
SUBJECT bWIT IMS CHK'O DATE i
0 h N & W ha n Q A Wen N $ & ACIS.
j ff. [.22s t$ E X
y (A M TA M k hb)
(f(d
( f. B-I Tk va 6 - 10 )
i
(
P
(
7s/4 12 TMI borated water tank Overturning Moment Capacity 03-21-98 12:48:14
@ You are now executing program TANKER
@ A program to estimate the seismic @
@ capacityofverticalstoragetanks @
e
21/4 63 l
l eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeese eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees TMI borated water tank Overturning Moment Capacity 03-21-98
\\
eesseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee 1
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee l
l l
l l
T ANK D ATA RADIUS
= 1.9800EH)2 l
SHELL THICKNESS
= 4.2100E-01 l
BOTTOM PLATE THICKNESS = 2.5000E41 SHELL YOUNG'S MODULUS = 2.8000EH)7 ANCHORAGE D ATA NUMBEROF ANCHORBOLTS 40
=
ANCHOR BOLT DIAMETER
= 2.0000E+00 EXPOSED LENGTH OF BOLT = 3.8000E+01 TOTAL LENGTH OF BOLT
= 9.1000E+01 BOLT YOUNG'S MODULUS
= 2.8000E+07 l
PREC ALCUL ATED D ATA
~
EFFECTIVE FLUID WElGHT = 3.7770E+01 TANK SHELL CRITICAL STRESS = 2.4650E+04 l
LIMIT ON BOLT CAPACITY = 3.6300E+05 i
NET VERTICAL BASE REACTION = -6.1200E+04 1.
l ITE R A TIO N PARAMETERS MAXIMUM # OF ITERATIONS = 200 CONVERGENCE TOLERANCE = 1.00
)
i l
I i
tt/aP 89 TMI borated water tank Overturning Moment Capacity 03-21-98 12:48:14
...c.................................................................................
..............e.....e....e..e....e.e.e......
INTERMEDI ATE RESULTS ITER # NEUTRAL AXIS PS PB PL PSUM XNORM 1
1.5708E400 -4.1095E+06 4.1089E+05 9.3404E404 -3.6053E+06 -3.5441E+06 2
1.0472E+00 -2.8144E+06 1.5760E+06 1.6113E+05 1.0773EM6 -1.0161E+06 3
7.2273E-01 -1.9625E+06 4.0781E+06 2.2622E+05 2.3418EM6 2.4030EM6 4
8.9566E-01 -2.4201E+06 2.3937E+06 1.8811E+05 1.6677E+05 2.2797E+05 5
9.7339E-01 -2.6232E+06 1.9258E+06 1.7367E+05 -5.2370E+05 -4.6250 EMS 6
9.3509E-01 -2.5233E+06 2.1421E+06 1.8062E+05 -2.0061E+05 -1.3941E+05 7
9.1552E-01 -2.4721E+06 2.2653E+06 1.8429E+05 -2.2572E+04 3.8628EM4 8
9.2534E 01 -2.4978E+06 2.2025E+06 1.8243EM5 -1.1293E+05 -5.1726E+04 9
9.2044E-01 -2.4850E+06 2.2336EM6 1.8336E+05 -6.8092E+04 -6.8920E+03 10 9.1799E-01 -2.4786E+06 2.2493E+06 1.8382E+05 -4.5419E+04 1.5781E+04 11 9.1921E-01 -2.4818E+06 2.2414E+06 1.8359E+05 -5.6777E+04 4.4235E+03 12 9.1983E-01 -2.4834E+06 2.2375E+06 1.8347E+05 -6.2440E+04 -1.2400E+03 13 9.1952E-01 -2.4826E+06 2.2395E+06 1.8353E+05 -5.9610E+04 1.5903E+03 14 9.1967E-01 -2.4830EM6 2.2385E+06 1.8350E+05 -6.1025E+04 1.7508E+02 15 9.1975E-01 -2.4832E+06 2.2380E+06 1.8349E405 -6.1732EM4 -5.3234E+02 16 9.1971E-01 -2.4831E+06 2.2382E+06 1.8349E+05 -6.1379EM4 -1.7870E+02 17 9.1969E-01 -2.4831E+06 2.2384E+06 1.8350E+05 -6.1202E+04 -2.0938EM0 18 9.1968E-01 -2.4830E+06 2.2384E+06 1.8350E+05 -6.lll3E404 8.6703EMI 19 9.1969E-01 -2.4830E+06 2.2384E+06 1.8350E+05 -6.ll58E+04 4.2109E+01 20 9.1969E-01 -2.4831E+06 2.2384EM6 1.8350E+05 -6.1181E+04 1.9438E+01 21 9.1969E-01 -2.4831E+06 2.2384E+06 ' 1.8350E+05 -6.1191E+04 8.5781E+00 22 9.1969E-01 -2.4831EM6 2.2384EM6 1.8350E405 -6.1197E+04 3.4844E+00 23 9.1969E-01 -2.4831E+06 2.2384E+06 1.8350E+05 -6.1200E+04 4.5313E-01
Ofd O5 eeeeeeeee.eeeeeeeeee,eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee seeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee TMI borated water tank Overturning Moment Capacity 03-21-98 12:48:14 seeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee+++eseo eseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees.
RESULTS OF AN ALYSIS (1) NEUTRAL AXIS LOCATION:
DEGREES RADIANS.
52.6945 9.196?E-01 (2) TENSILE FORCES IN ANCHOR BOLTS:
DOLT # REF. ANGLE (DEGREES)
FORCE 1
180.0000 1.3184E+05 2
171.0000 1.3083E+05 3
162.0000 1.2782 EMS 4
153.0000 1.2289E+05 5
144.0000 1.1616EM5 6
135.0000 1.0780E+05 7
126.0000 9.8002E+04 8
117.0000 8.7018EM4 9
108.0000 7.5118EM4 10 99.0000 6.2592E+04 11 90.0000 4.9751E+04 12 81.0000 3.6909E+04 13 72.0000 2.4384E+04 14 63.0000 1.2483EM4 15 54.0000 1.5004E+03 (3) DIRECT FORCES AT TANK BASE:
LONGITUDINAL FORCE IN SHELL
= -2.483 IBM 6 SUM OF ANCHOR BOLT FORCES
= 2.2384EM6 BOTTOM PLATE HOLDOWN FORCE
= 1.8350EM5 TOTAL = -6.1200EM4
)
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(4) RESTORING MOMENT.
FROM LONGITUDINAL FORCES IN SHELL= 4.5196E@8 FROM ANCHOR BOLTS TENSILE FORCES = 2.7984E+08 FROM BOTTOM PLATE HOLDOWN FORCE = 1.6569E47
)
1 TOTAL = 7.4837EM8
$23 $o
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TMI borated water tank Overturning Moment Capacity 03-21-98 l
12:48:14 ADDITION AL RESULTS:
MAXIMUM LENGTH OF UPLIFTED BOTTOM PLATE = 9.8671E+00 MAXIMUM UPLIFT DISPLACEMENT
= 1.3639E-01 MAXIMUM FIBRE STRESS IN BOTTOM PLATE = 5.8837E+04 i
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